How to rename active or first texture slot of a material from script
I realize I just posted the question but I solved this myself not long after. You can also rename the texture names and texture image names with this script by modifying the block of code that renames materials like so:

        if self.rename_material:
            if ob.material_slots:
                for m_slot in ob.material_slots:
                    if m_slot.material:
                        if m_slot.material.users == 1:
                            if (self.rename_use_prefix
                            and self.prefix_material):
                                m_slot.material.name = self.rename_prefix + name
                            else:
                                m_slot.material.name = name
                        if m_slot.material.texture_slots:
                            ~~~~VVV Added The Following VVV~~~
                            if(len(m_slot.material.texture_slots) &gt; 0):
                                m_tex = m_slot.material.texture_slots[0]
                                m_tex.texture.name = name
                                m_tex.texture.image.name = name


Obviously there's some checks that could be done such as number of users and such. I'll post back as I polish the script.